Question: Solve for $y$. $-3 = 7\left(y-\dfrac97\right)$
Answer: Let's divide and then add to get $y$ by itself. $\begin{aligned}-3 &= 7\left(y-\dfrac97\right) \\ \\\\\\ \dfrac{-3}{{7}} &= \dfrac{7\left(y-\dfrac97\right)}{{7}} ~~~~~~~\text{divide each side by } {7}\\ \\\\ \dfrac{-3}{{7}}&=\dfrac{\cancel{7}\left(y-\dfrac97\right)}{\cancel{{7}}} \\ \\ \dfrac{-3}{{7}} &= y-\dfrac97\end{aligned}$ $\begin{aligned} -\dfrac37&=y-\dfrac97\\ \\ -\dfrac37 {+\dfrac97}&= y-\dfrac97{+\dfrac97}~~~~~~~{\text{add }\dfrac97} \text{ to each side} \text{ to get } y \text{ by itself }\\ \\ -\dfrac37{+\dfrac97}&= y-\cancel{ \dfrac97} {{+}\cancel{{\dfrac97}}}\\ \\ -\dfrac37{+\dfrac97}&=y\end{aligned}$ The answer: $y={\dfrac67}$ Let's check to make sure. $\begin{aligned} -3 &= 7\left(y-\dfrac97\right) \\\\ -3 &\stackrel{?}{=}7\left({\dfrac67}-\dfrac97\right) \\\\ -3&\stackrel{?}{=} 7\left(-\dfrac37\right) \\\\ -3 &= -3 ~~~~~~~~~~~~~~\text{Yes!} \end{aligned}$